The anti-NK model and minimum wages

I present a simple model that has exactly the opposite predictions to the standard New Keynesian model: if the central bank sets the nominal interest rate too high (too low), that will cause an increase (a decrease) in output and employment.

If you think that an increase in the minimum wage will cause increased employment, because firms have monopsony power in the labour market, you will like my model.

The intuition is straight out of the first-year micro textbook. If the price of X is sticky, and is above the competitive equilibrium (monopoly), then the quantity of X bought-and-sold is determined by the demand for X. If the price of X is sticky, and is below the competitive equilibrium (monopsony), then the quantity of X bought-and-sold is determined by the supply of X. The short side of the market determines quantity traded. Q = min{Qd;Qs}.

Here is my anti-NK model:

All firms produce exactly the same variety of output, so the output market is perfectly competitive. (In the NK model each firm produces a different variety of output, and has monopoly power in the output market, and faces a downward-sloping demand curve.)

Each firm employs a different variety of labour, and has monopsony power in the labour market, and faces an upward-sloping labour supply curve. (In the NK model all firms employ the same variety of labour, so the labour market is perfectly competitive.)

If you insist on a representative agent model: the representative agent in my model has Dixit-Stiglitz preferences for employment, and so prefers to sell labour to a variety of firms. (The representative agent in the NK model has Dixit-Stiglitz preferences for consumption, and so prefers to buy output from a variety of firms.)

Prices are perfectly flexible in my model, but wages are sticky, with a Calvo Phillips curve for wage inflation. (Wages are perfectly flexible in the NK model, but prices are sticky, with a Calvo Phillips curve for price inflation.)

In my model profit-maximising firms set wages as a markdown under the price times the marginal product of labour: W = (1-m)P.MPL. (In the NK model, profit-maximising firms set prices as a markup over marginal costs: P = (1+m)W/MPL.)

In my model profit-maximising firms employ as much labour as they can buy, if they cannot change their wage. (In the NK model profit-maximising firms produce as much output as they can sell, if they cannot change their price.)

Everything else is identical between my model and the standard NK model.

The key equation in my model is the leisure-Euler equation. The ratio of current desired leisure over expected future leisure is a negative function of the nominal interest rate minus expected wage inflation.

Suppose the central bank sets the nominal rate of interest too low for one period. The representative agent wants to consume more leisure today, and less leisure in future. So labour supplied falls today. Firms would like to raise wages, but cannot, because wages are sticky. So employment falls today, which means output falls too, and prices rise to clear the output market.

Suppose the central bank sets the nominal interest rate too high for one period. The representative agent wants to consume less leisure today, and more leisure in future. So labour supplied rises today. Firms would like to cut wages, but cannot, because wages are sticky. So employment rises today, which means output rises too, and prices fall to clear the output market.

In my model, the consumption-Euler equation, which is the key equation in the standard NK model, is not important. It plays no role in determining output and employment. The current price level instantly adjusts, relative to the expected future price level, and the nominal interest rate, to ensure that it is always satisfied at any level of output.

In the standard NK model, the leisure-Euler equation, which is the key equation in my model, is not important. It plays no role in determining output and employment. The current wage level instantly adjusts, relative to the expected future wage level, and the nominal interest rate, to ensure that it is always satisfied at any level of employment.

In my model, a binding minimum wage law will increase employment and output. It reduces firms' monopsony power.

In the standard NK model, a binding maximum price law will increase output and employment. It reduces firms' monopoly power.

Comments

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These are quite interesting. What would happen if they were sticky in only one direction? One was sticky in one direction and the other in the other direction? What would happen if half the firms had sticky prices and half had sticky wages?

Lord: if P (or W) is sticky in only one direction, you get classical results if monetary policy moves P (or W) in the other direction: no change in L or Y. I don't know what would happen in the other cases. Too tricky.

JW: all of the above. In roughly this order (starting with the most important):

3 (above all the others)

2 (and to clarify the logic even for those who think they understand the standard explanations, because this one is hard to separate from 3)

5

1 and 4. Even though monopoly power is more common than monopsony (I think), we can't say there never is monopsony. Sometimes the supply side bites.

But there is one thing missing from your list: I want to create cognitive dissonance for those who think the NK model (or something similar) is roughly right, and who also believe that minimum wages increase employment because of monopsony power.

And it is a good thing to confront that cognitive dissonance. I suffer from it myself, when I want to believe both the NK model is roughly right and Milton Friedman's plucking model. I did a post on that once. This one is closely related.

JW: Here's another motive (though I did not model this explicitly): if you believe that nominal wages are about as sticky as prices, or even more sticky (and that is a very plausible assumption), then you need to be really careful about assuming either monopsony or perfect competition in the labour market, if you want to get NK results. Your only safe assumption is monopoly power in the labour market.

JW, when Nick writes "I want to create cognitive dissonance for those who think the NK model (or something similar) is roughly right, and who also believe that minimum wages increase employment because of monopsony power."

So that's Nick on the left... the representative NK victim is seated on the right:

You’ve taken a microeconomic idea (firms face “an upward-sloping labour supply curve”) and extended it to the world of macro. Always a dangerous ploy and I suggest the latter micro idea is irrelevant at the macro level.

What IS RELEVANT at the macro level is that as employment rises, and dole queues shrink, the quality of labour available to firms from the dole queue declines. And when the revenue product of that labour declines to the union wage / min wage etc, then further rises in demand are inflationary. I.e. the economy has hit NAIRU.

Ralph: the standard NK model has taken a micro idea (firms face a downward-sloping demand curve) and extended it to the world of macro.

Starting in equilibrium:
If an individual firm raised its price, would all its customers quit? No. It faces a downward-sloping demand curve.
If an individual firm cut its wage, would all its workers quit? No. It fases an upward-sloping labour supply curve.

Do the Dixit-Stiglitz preference for employment actually do any work here? In the most basic New Keynesian model without a fiscal authority, the Dixit-Stiglitz preferences for consumption don't have any effect on the optimal monetary rule, I believe - only a fiscal authority can correct the underproduction of goods caused by monopoly power (e.g. by subsidy via lump sum tax). So does it actually do anything here, when the preferences are over labor? I don't think so.

I ask because it seems likely a very silly assumption beyond for expositional purposes.

In the standard NK model, the only role played by Dixit-Stiglitz (or similar) preferences is to enable you to personify the representative agent. If you instead assumed that there are different people, with different preferences, so different people prefer to consume different goods, you would get roughly the same results. Suppose we all have a different favourite restaurant, but will switch to our second favourite if our favourite raises its price too much.

In my model, it's similar. Suppose we each have our (different) favourite place to work, but will switch to our second favourite if our favourite cuts its wage too much. That makes more sense than Dixit-Stiglitz preferences for every agent. But it would be roughly similar.

My Ph.D. is in cab driving (NY-Chi-SF) so your post is a little too dense for me -- here is my latest eighth-grade math take on the same subject (in the American context anyway). I think you'll like it -- even if a little long:

On the bottom end of the wage scale we may find a "DISCOUNT wage effect": wherein weak bargaining power leaves wages below -- in the American labor market probably far below -- what consumers would have been willing to pay: meaning that today’s consumers are getting a – probably hugely serious -- bargain.

On the other end of the wage scale we might find examples of a wage "PREMIUM wage effect": where consumers are pressured by market conditions to pay much more than the seller would have been willing to accept if there were sufficient competition or whatever: meaning consumers are getting a -- possibly hugely serious -- skinning.

If a deeply discounted wage is raised -- in Obama's case ...
... to still below LBJ's 1968 minimum wage ...
... almost double the per capita income later (!) ...
... stretched out over three years (agh!!!) ...

... I think consumers are more likely to drop some spending on premium wage products (where they are being skinned) in order to continue purchasing the still deeply DISCOUNTED wage products (and therefore still very much comparative bargains.

Even were today's federal minimum of $7.25 doubled to $15 they would still end up paying only as much as they would probably have been willing to pay in the first place – still a COMPARATIVE bargain with PREMIUM wage made products.
* * * * * * * * * * * * * * * * * * * * * * *
When I was a gypsy cab driver in the Bronx, back in the late 1970s, the (legit — with medallions, etc.) yellow cabs raised their meters and we raised ours in step with theirs. Everybody agreed that this did not hurt business. I also heard from the veteran drivers that the last meter raise did cost a lot of business — I was new (finally got my driver’s license at age 32).

In any market, selling anything, you never know for sure what the customer will pay until you test. Does this chart below look like the federal minimum wage has been much tested (OVER MULTIPLE GENERATIONS!!!)?

TMF: thanks. Yep, when we play with models like this, we also learn a lot more about how they work. What role each assumption plays in the results. We need to do this more.

"This could be true of any model where you assume monopsony in the labor market, right ? You wouldn't necessarily need your other assumptions ?"

That's probably roughly right, in general. Though you could presumably always rig up some of the other assumptions to stop you getting that result.

Min: I'm not sure what you are asking. If wages are sticky, and if they are generally below the competitive equilibrium (i.e. monopsony power is common), then the NK model won't work very well. My model here is just an extreme case of that, where my results are the opposite of the NK results.

Denis: in a monopolistic labour market, workers usually find it hard to find employers at current wages. In a monopsonistic labour market, employers usually find it hard to find workers at current wages. To my mind, it looks like a bit of both. Depends on the job and the worker. But it's hard to say for sure, because both employers and workers adjust quality, if wage won't adjust.

Nick: in my estimation, if we institute a minimum wage that mimics a bargaining demand somewhere in the neighborhood of what the consumer is willing to pay, we should no longer consider the labor market effectively monopsonistic (if I understand what you are saying).

Have to remember too that the labor component of the market price may be a small as one-fourteenth in the case of Wal-Mart -- which can potentially leave lots of wage costs room.

Since I don't like the NK model much and I also don't believe in labor market monopsony (much, not in the min wage sector) I think I get a free pass here. But, it did make me think of something: how would a standard NK or anti-NK model work where instead of Calvo pricing you simply impose the constraint that once nominal wages rise they cannot ever fall again, rational expectations, good prices flexible, and all that? That might actually require some monopsony power for it to work, or at least for me to think about it in words.

Obviously if there's a bad shock real wages may not fall enough to clear the labor market - the short side is labor demand. If there is a positive shock firms would like to hire more workers and to do so would want to raise wages... but they anticipate that once they raise them wages, they won't be able to bring them back down when shock goes away, or a bad shock occurs. So present value and all and no (smaller) increase in wages - the short side is labor supply. It'd be a model with an "endogenous minimum wage" and firms expecting movements in that wage. It might look similar to this.

To me the trick is in assuming everyone believes the bank made a mistake in a certain direction and that it will be corrected the next period since they might as well believe it didn't make a mistake, made a mistake in the opposite direction, or that it will be compounded, or overcorrect, though on average it must believe something. If the unexpected happens, one just assumes they thought the opposite so it is somewhat short on explanatory power, smacking of self fulfillment, without some independent confirmation. Somewhat begging the question of how they arrived at that belief other than by random walk.

An interesting quirk about monopsony in the labor market, is that _if_ you believe that firms are imperfectly competitive in both the labour and the product market (and this is a plausible assumption in many cases), then enacting a minimum wage (or strengthening unions, etc.) is likely to have bad consequences, due to a second-best problem. Imperfectly competitive firms need to charge monopoly prices in order to defray their fixed costs, but they are highly limited in how much monopoly rent they can extract in the long run, due to the possibility of additional entry. If the firm has bargaining power in both markets, it will charge a monopoly rent from both, depending on the inverse elasticities it faces, and this will lead to a relatively efficient outcome (deviations from the competitive case are small). But if it's forced to set perfectly competitive wages, it will have to defray its costs in the product market alone. This then results in a combination of higher deadweight losses and less product variety.

Note that this only applies when markets are contestable; the element that disciplines firms so that they will extract a known amount of monopoly rent is the threat of entry.

Moi: "What if you believe that some wages (a sizable minority) are sticky, and that they tend to be on the low side, but above the minimum wage?"

Nick Rowe: " I'm not sure what you are asking. If wages are sticky, and if they are generally below the competitive equilibrium (i.e. monopsony power is common), then the NK model won't work very well."

Thanks, Nick. :)

What I had in mind were the graphs of year to year changes in nominal wages, in which most wage changes exhibit a normal curve, which indicates wage flexibility, but there is a spike at zero change, which indicates stickiness. There is clear difference between flexible and sticky wages; the distinction is not fuzzy. At all.

Then, given that only some wages are sticky, I guessed that they would tend to be on the low side, as workers with wages on the high side have more bargaining power.

"Nick Rowe is not personally taking a stand on the minimum wage debate. However, he argues that for those economists who DO think employment effects will be minimal (or even positive) from hiking the minimum wage, the theoretical argument they usually give to explain the result would ALSO mean that if the central bank raised interest rates, then this too would promote employment. So, to extend Nick's analysis, this means that we shouldn't see the same economists (a) supporting low interest rate policies and (b) supporting a hike in the minimum wage."

Does that work Nick?

And, if it does, what happens when someone says, "Liquidity trap, your argument is invalid." ?

Bob: basically yes. Positive effects from minimum wage due to monopsony power go along with positive effects on employment from raising interest rates. Definitely a tension between standard views on interest rates, and arguing that raising minimum wages is a good thing due to monopsony.

You lost me on the liquidity trap bit.

I'm not a fan of minimum wages. There are better ways. Stephen Gordon has also done some good posts saying that minimum wages are not a good anti-poverty policy.

Keshav: it is simpler to build a model if you have either prices or wages sticky, but not both sticky. Most of us believe that both prices and wages are sticky, but might disagree on which is stickier. An NK model with prices stickier than wages would behave roughly the same as an NK model with only prices sticky.